# Partition of a group

## Definition

A **partition** of a group is an expression of the group as a set-theoretic union of subgroups, with pairwise trivial intersections.

The partition is said to be *nontrivial* if it uses more than one subgroup, or equivalently, if all the subgroups are proper.

Note that any nontrivial partition must involve at least three subgroups. `Further information: Union of two subgroups is not a subgroup unless they are comparable`

Not every group admits a nontrivial partition. `Further information: group admitting a nontrivial partition`